Definition:Factorial Experiment
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Definition
A factorial experiment is an experiment structured so that several different types of treatment can be compared, at different qualitative or quantitative levels.
The design will allow the experimenter to see whether the effects of each factor is additive, or whether they interact.
Results are typically analysed by partitioning the between-treatments sum of squares in an ANOVA exercise into:
and:
Designs may involve any number of factors and any number of levels of each factor.
In a randomized block design, every factor-level combination appears once in each block.
Factor
One of the different types of treatment being compared in a factorial experiment is known as a factor.
Main Effect
In a factorial experiment, the main effects of factors are those which are additive.
Interaction
In a factorial experiment, factors are said to interact if their effects are not directly additive.
Examples
Chemical Process
A typical factorial experiment is one which measures the yield of a chemical process.
Let factor $A$ be three different temperatures: $100 \cels$, $150 \cels$ and $180 \cels$.
Let factor $B$ be two different pressures: $1$ and $2$ standard atmospheres.
If:
- the yield were to increase as temperature increases at the lower pressure
but:
- the yield were to decrease as temperature increases at the higher pressure
then the factors $A$ and $B$ interact.
Also see
- Results about factorial experiments can be found here.
Historical Note
The technique of factorial experiments was pioneered by Frank Yates in $1934$.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): factorial experiments
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): factorial experiments